Floating Lenses

We now focus our attention on the case of two non-miscible liquids A and B floating on one another. The liquid substrate B is assumed to be denser (it has a density ps and a surface tension 75). The liquid A (density Pa Pb and surface tension 7 ) is laid down on top. The interfacial tension 7 5 is also assumed to be known (it can be measured, as we will show shortly). 

---

Films from low energy liquids on water substrate have been studied in [521,543,544] and their thickness were measured employing an adsorption method. These along with the results of many other authors [e.g. 204] indicated that at equilibrium most organic liquids formed monolayers at the water surface. The increase in liquid pressure lead to formation of drops from the organic phase in the form of floating lenses. In the series of saturated... 

During the time of preequilibration part of the crude oil formed a stable oil in water emulsion (more pronounced for AOS). Prior to extracting the liquid from the double concave meniscus, it was observed that floating lenses of crude oil were spread upon the foam surfaces. 

Finally, floating lenses of liquids offer a pabulum for the development of theory to describe the involved curvatures mathematically. Comparison with experiments allows the establishment of the three contact angles, see for Instance refs. 2 3). Aveyard and Clint" ) reviewed the stability and capillarity of floating droplets in the presence of surfactants. 

Once again, small drops adopt spherical cap shapes, and larger drops form fiat lense shapes. These floating lenses are subject to an Archimedean upthrust. Their thickness can be discovered by measuring their radii as a function of volume. The spreading parameter 5 = 7b — (7a + 7ab) can be deduced from the formula pe /2 = —S, where... 

The contact angles can be determined also by the technique of floating lens, which is widely used in the study of black films from hydrocarbons in aqueous medium [5]. However, in foam films such a lens cannot be always formed. 

This inclndes the cases of a bnbble/droplet nnder a plate (Fignre 5.7a), the two surfaces of a floating lens (Figure 5.7b), and any kind of sessile or pendant droplets/bnbbles. Snch a meniscns is a part of a sphere when the effect of gravity is negligible, that is, when... 

In chapter 2, we will describe a simple technique for determining the interfacial tension jab by measuring the thickness of a floating lens. 

Application Measuring ab a Ruler. Measuring the radius of a floating lens gives its thickness if the volume is known. The parameter S can then be deduced from equation (2.46). Since in general 7 and p are specified for a given liquid, ab is readily deduced. 

The equilibrium shape of a liquid lens floating on a liquid surface was considered by Langmuir [59], Miller [60], and Donahue and Bartell [61]. More general cases were treated by Princen and Mason [62] and the thermodynamics of a liquid lens has been treated by Rowlinson [63]. The profile of an oil lens floating on water is shown in Fig. IV-4. The three interfacial tensions may be represented by arrows forming a Newman triangle ... 

At the Endeavor (formerly Elura) Mine (43 km NNW of Cobar), the main lens of the Elura Zn-Pb-Ag orebodies is subcropping with a small patch of gossanous float present in an essentially flat landscape. There Pb in saprolite (>50 ppm in an area 1.4 x 1.0 km) and lag (>50 ppm in an area 2.5 x 1.6 km) define the underlying mineralisation. However Zn in soil is anomalous for >1 km to the southwest of the main lens (Lorrigan... 

If we consider the equilibrium of a lens floating on the surface of a mutually saturated liquid the following relationships evidently obtain... 

Antonow s rule is tlius only exact when the two mutually saturated liquids possess the same density. The observed values of cti2 should in general be slightly less than those determined from — In the case of oleic acid floating on water Devaux obtained a lens thickness of OT cm. Since p — 0 90 the interfacial surface tension should be O M dyne less than the value obtained with the aid of Antonow s rule. 

We developed an experimental procedure that can be applied to highly viscous polymer blends. In the DSM micro-extruder [6], polymers are blended in the melt, at the desired temperature and pressure, and injected into a small capillary tube which is immediately sealed with a floating plug. This capillary cell is placed in a small window autoclave and a laser beam enters the capillary cell at the lens-shaped bottom end. The intensity of the light scattered by the polymer system is recorded at two scattering angles (as a function of pressure and temperature). 

Micromass has applied this new hexapole technology to a fast scanning magnetic sector multiple-collector instrument (Fig. 8.6). The source is at ground potential so most of the lens system and analyzer float at —6 kV. The ions are extracted into the hexapole through a sample cone with a 1.1-mm orifice, a 0.8-mm orifice skimmer cone, and finally a 2-mm orifice transfer lens held at —400 V. The hexapole is inclined to prevent line-of-sight transmission and damage to the detectors from the source. A lens system transfers the ions into the mass analyzer. 

When a lens of one liquid floats on the surface of another (Fig. 9.VIII G) there are three contact surfaces, gas /liq. 1, gas /liq. 2, and liq, 1 /liq. 2, The three interfacial tensions, Oi, 02, and oi2 will be in eqiMbrium if lines representing them in magnitude and direction form a closed triangle, usually called Neumann s triangle. The relation ... 

Not discussed here, but also equally feasible is the calculation of the equilibrium profiles of sessile and pendent lenticular configurations—for example, drops of an immiscible liquid floating on an interface (like oil on water) form a sessile lens as illustrated in Fig. 

In humans, a contact lens lies in the conjunctival sac of the eye. In a closed eye, this sac is a slitlike space between the conjunctiva-covered eyeball and the eyelids. Contact lenses are small polymer bowls that float on tears superficial to the corneal eye layer and correct existing visual deficiencies similarly to glasses. While the idea of the contact lens was formulated as early as 1508, it was not until the 1800s that contact lenses became a reality. Hard plastic contact lenses were invented around 1936, and although soft lenses were invented in 1960, they were not available on the commercial market until 1971. 

Figure 1.14(a) shows the phase prism of the system water-oil-non-ionic surfactant (already shown in Fig. 1.3) together with the temperature dependence of the interfacial tensions (Fig. 1.14(b)). As discussed in Section 1.2.1, at low temperatures, non-ionic surfactants mainly dissolve in the aqueous phase and form an oil-in-water (o/w) microemulsion (a) that coexists with an oil-excess phase (b). Thus, for temperatures below the temperature T the interfacial tension microemulsion separates into two phases (a) and (c) at the temperature T) which, in turn, leads to the appearance of the three-phase body. Thus, three different interfacial tensions occur within the three-phase body, namely the interfacial tension between the water-rich and the surfactant-rich phase crac, between the oil-rich and the surfactant-rich phase oyc, and between the water-rich and the oil-rich phase uab. However, the latter can only be measured if most of the surfactant-rich middle phase (c) is removed, which then floats as a lens at the water/oil interface. Increasing the temperature one observes that the three-phase body vanishes at the temperature Tu, where a water-in-oil (w/o) microemulsion is formed by the combination of the two phases (c) and (b). Therefore, at temperatures above Tu the interfacial tension crab refers to the interface between a w/o-microemulsion and a water-rich excess phase. 

The liquid perfluorocarbons, with specific gravities between 1.76 and 1.94, are denser than vitreous and are helpful in flattening the retina when vitreous is present. If a lens becomes dislocated into the vitreous, a perfluorocarbon liquid injection posteriorly will float the lens anteriorly, facilitating surgical retrieval. This liquid can be an important tool for flattening and unroUing severely detached and contorted retinas such as those found in giant retinal tears and proliferative vitreo-retinopathy but are potentially toxic if it remains in chronic contact with the retina. 

Fig. 4.6 The strange image of a dandelion floating on the surface of water is a consequence of the bent interface between the water and the dandelion, which acts as an optical lens. (Authors own work)...

Polymeric soft contact lenses came into existence in the 1950s (12]. Otto Wich-terle discovered the hydrogel poly(hydroxyethyl methacrylate) (HEMA), a transparent, soft, hydrophilic material that could be used to prepare contact lenses, Wichterle utilized a free radical polymerization of the HEMA monomer (including cross-linker, solvent, initiator, and stabilizer) with either thermal or ultraviolet initiation of the reaction. Initially, the len.ses were produced via spin casting, which involved the use of a concave mold that is spun at a particular rate. The rate of the mold spin determines the resultant lens power (13). After production of the lens in the mold, the lens would be hydrated from the mold in a warm water solution. Once hydrated, the lens would float free from the mold. Each lens is inspected for rips, tears, and clarity. Finally, the lens is packaged, sterilized, and boxed for shipping. The surface quality of the mold determines the surface chemistry and morphology on the anterior surface of the lens produced. 

OECD Method 221 [34] has been available since 2006 and is a growth inhibition test for Lemna minor, the small water lens. The test uses a defined number of fronds of Lemna plants which float on top of an aqueous sample and are incubated for 7 days increase in the number of fronds and increase in biomass are measured. Like... 

---